Related papers: Description of dynamics of stock prices by a Lange…
We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription.…
This paper tends to define the quantitative relationship between the stock price and time as a time function. Based on the empirical evidence that the log-return of a stock is the series of white noise, a mathematical model of the integral…
Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
Characterizing temporal evolution of stock markets is a fundamental and challenging problem. The literature on analyzing the dynamics of the markets has focused so far on macro measures with less predictive power. This paper addresses this…
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for…
We present a new, recursive approach to stochastic inflation which is self-consistent and solves multiple problems which plagued a certain number of previous studies, in particular in realistic contexts where the background spacetime is…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…
Statistical dynamics of financial systems is investigated, based on a model of a randomly coupled equation system driven by a stochastic Langevin force. Anticorrelations of price returns, and subdiffusion of prices is found from the model,…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the…
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the L\'evy flights in two dimensions (2D). The efficacy of our proposed model is…
In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable…
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…